If the length of a rectangle prism is doubled, it’s width is tripled, and it’s height remains the same, what is the volume of the new rectangle prism?

D would be your answer

Step-by-step explanation:

If you double all of the dimensions of a rectangular prism, you create a similar prism with a scale factor of 2.  The surface area of the similar prism will increase as the square of the scale factor (22 = 4) and the volume will increase as the cube of the scale factor (23 = 8).

Here's why.  Let the dimensions of the original prism be a, b, and c.  Its volume is:

V = a*b*c

Now double all of the dimensions: 2a, 2b, 2c.  The new volume is:

Volume = 2a*2b*2c = 2*2*2*a*b*c = 23*(a*b*c)

Since a*b*c is the volume of the original prism, the volume of the larger prism is 23=9 times larger.

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